(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

I'm getting different results when choosing my u & dv for Integration by Parts on the following integral:

[tex]\int 2x^3 e^x^2 dx [/tex]

(Note, the exponent on 'e' is x^2)

This yields the correct solution:

u = [tex]x^2[/tex]

dv = [tex]2x e^x^2 dx [/tex]

du = [tex]2xdx[/tex]

v = [tex]e^x^2[/tex]

However, I have tried using this instead (*)

u = [tex]2x^3[/tex]

dv = [tex]e^x^2 dx [/tex]

du = [tex]6x^2 dx[/tex]

v = [tex](e^x^2) / 2x[/tex]

and this is yielding the incorrect solution (see 3.)

2. Relevant equations

Integration by Parts:

[tex]\int udv = uv - \int vdu [/tex]

3. The attempt at a solution

The correct solution turns out to be

[tex] x^2 e^x^2 - e^x^2 + C[/tex]

When I use my other choice of variables (*), I get (using IBP)

[tex] \int 2x^3 e^x^2 dx = 2x^3 e^x^2 / 2x - \int e^x^2 / 2x * 6x^2 dx [/tex]

which leads to:

[tex]x^2 e^x^2 - 3/2 e^x^2 + C [/tex]

which is different from the other choice of variables.

I've looked over both choices of variables, and I don't know why the second choice (*) comes up with a different solution.

Thanks for the help!

**Physics Forums | Science Articles, Homework Help, Discussion**

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Integration by Parts - Choice of variables

**Physics Forums | Science Articles, Homework Help, Discussion**